What Planck does not tell us about inflation

TL;DR

This paper examines how Planck data constrains multi-field inflation models, especially focusing on reheating and isocurvature effects, and finds that multi-field inflation remains a viable theory despite current constraints.

Contribution

The paper analyzes four multi-field inflation scenarios, extending previous studies by considering arbitrary isocurvature evolution and constraining these models with Planck data.

Findings

Planck bispectrum limits only certain parameter regions.

Reheating hypersurface curvature is tightly constrained.

Multi-field inflation remains a plausible model.

Abstract

Planck data has not found the 'smoking gun' of non-Gaussianity that would have necessitated consideration of inflationary models beyond the simplest canonical single field scenarios. This raises the important question of what these results do imply for more general models, and in particular, multi-field inflation. In this paper we revisit four ways in which two-field scenarios can behave differently from single field models; two-field slow-roll dynamics, curvaton-type behaviour, inflation ending on an inhomogeneous hypersurface and modulated reheating. We study the constraints that Planck data puts on these classes of behaviour, focusing on the latter two which have been least studied in the recent literature. We show that these latter classes are almost equivalent, and extend their previous analyses by accounting for arbitrary evolution of the isocurvature mode which, in particular, places important limits on the Gaussian curvature of the reheating hypersurface. In general, however, we find that Planck bispectrum results only constrain certain regions of parameter space, leading us to conclude that inflation sourced by more than one scalar field remains an important possibility.